In an SLR, the light bouncing off the mirror goes through a pentamirror or pentaprism before being reflected to the viewfinder. However, it seems to me that it would be possible to project an image to the viewfinder simply by using two mirrors, the upper one at a complementary angle to the lower one, much like a simple periscope.

Such a system might have benefits in terms of light transmission, as the light is only reflecting off 2 surfaces instead of 5, leading to a brighter viewfinder. This is such an obvious thing that I feel I must have misunderstood the purpose of the pentamirror/pentaprism.

Can anyone elaborate on why exactly such a complex path of reflecting surfaces is needed in an SLR?

1 Answer
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It's important to realize that you don't actually look directly through the lens with an SLR! If you did, a periscope style arrangement would do just fine.

What you are actually doing is looking at an image projected onto the focussing screen by the lens. This image is flipped left/right and up/down by the lens, and then up/down again by the main mirror.

This leaves the image flipped left-right. If you get chance to play with a medium format camera with waist level viewfinder (which amounts to just looking at the focussing screen through a tunnel) you'll see the image flipped left/right, which makes it difficult to use if you're not used to it.

To avoid this difficulty and present the user with a normal looking view in the viewfinder without the left/right inversion requires a roof pentaprism/pentamirror. A roof pentaprism is where one of the surfaces is split like a vaulted roof in order to laterally flip the image. Note that there are only three (not five!) reflections inside the prism, it's only pentagonal as one of the unused faces is truncated to save weight.

@nitro2k01 there are two reflecting surfaces inside a regular pentaprism, but three inside a roof pentaprism. That diagram is side on and so doesn't show that one of the reflecting surfaces is split in two.
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Matt GrumMar 13 '14 at 14:27

Oh, I see. Thanks for the clarification.
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nitro2k01Mar 13 '14 at 14:29

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@ChinmayKanchi the short answer is that you have to project the image onto something to check focus. Early film SLR screens were ground glass, with a clear split prism in the centre. DSLR screens are laser etched glass with no focus aid but the principle is the same.
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Matt GrumMar 13 '14 at 15:22

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Most modern Film SLR screens are also laser etched glass with no focus aids either. But if you're going to manual focus, you really do want that split prism to help out.
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MichaelTMar 13 '14 at 18:03